Answer: x = 6
Step-by-step explanation:
Because we are given that the two figures are already similar, we can set up a proportional relationship to determine the value of x. Since the larger rectangle has a width of 21 and the smaller rectangle has a width of 7, those values can be used as the numerators in the proportion. Since the larger rectangle's length is x plus the additional 3 units on the smaller rectangle, x+3 and 3 can be used as the denominators in the proportion.
Next, we set up the proportion as follows:
[tex]\frac{21}{x+3} =\frac{7}{3}[/tex]
Then, you cross multiply to get the equation:
[tex]63=7x+21[/tex]
After solving down algebraically, you get the value of x to be 6.
I hope this helps!
